\(T=a/2\pi \) , \(a\)  is the linear acceleration. The first term determine the absorption rate and the second term
determine the induced and spontaneous emission rate. The Planck factor in the Eq. (REF ) ensures that the
particle detector perceive a thermal bath of temperature \(T\) . For a circularly rotating observer,
the Planck spectrum is replaced by several anonymous factors which impose non-thermality in the system [1]}.
In the RCPI, only the spontaneous radiative process occurs hence there is no use of the number densities in calculation
of the response function [2]}, [3]}, [4]}. Here we can write the form of
\(\mathcal {S}^{ ab } _ { jk }\)  as,
\(\mathcal {S}^{ ab } _ { jk }=A^{a b}\delta _{jk}-i B^{ab}\epsilon _{jkl}\delta _{3 l}-A^{a b}\delta _{3j}\delta _{3k}~,\) 
